The invention relates to the reconstruction of a three-dimensional image of an object from a set of projected two-dimensional images of said object obtained from different positions of an imaging apparatus around the object.
It has a particularly advantageous application in the medical field that involves the reconstruction of the internal structures of a patient under examination, particularly the reconstruction of angiographic images, i.e., the obtainment of images of vascular trees opacified by the injection of a contrast medium.
The invention can nevertheless have applications in other fields, particularly in nondestructive industrial testing, in which tests of the same type as the medical tests are conducted.
In the medical field, the projected two-dimensional images of the object, for example a patient""s head, are generally obtained by the rotation of an X-ray imaging apparatus that revolves around the object.
There are essentially two types of reconstruction algorithms in X-ray imaging.
A first type provides for a retroprojection and filtering calculation, or even a Fourrier transform reconstruction in several dimensions.
A second type, the one to the invention relates, involves iterative reconstruction methods, also referred to as algebraic. The principle of such an algebraic algorithm is well known to one skilled in the art and has already been the subject of many publications. We refer in particular to the article by GORDON, BENDER and HERMAN entitled, xe2x80x9cAlgebraic Reconstruction Technique for Three-dimensional Electron Microscopy and X-ray Photography,xe2x80x9d THEO. BIOL Journal 29, pages 471 to 781 (1970), or the book by Anil K. JAIN entitled xe2x80x9cFundamentals of Digital Image Processing,xe2x80x9d Prentice Hall Information and System Sciences Series, Thomas Kailath Series Edition, or French Patent Application No. 89 03606 or No. 89 16906.
Briefly, after a calibration of the apparatus used in order to determine, in particular, the parameters for the projection, into the projection planes of the acquired images, of an observed volume broken down into elementary volume elements or voxels (which calibration parameters form projection matrices), the algebraic image reconstruction algorithm is used to reconstruct the three-dimensional volume from these projected two-dimensional images. The basic principle of this algorithm is to initialize the voxels of the volume to a predetermined initial value, for example a null value, and to iterate the following operations a certain number of times: the projection of the voxels into the plane of each acquired image so as to obtain a virtual image, the determination of the difference between the projected volume (virtual image) and the corresponding acquired image, followed by the projection of this difference back into the volume. After a certain number of iterations, an estimated value representing the density of the contrast medium injected into the X-rayed vessels is obtained for each voxel, making it possible to display the three-dimensional cartography of these X-rayed vessels.
The acquired images generally have a resolution equal to 512, i.e., they comprise 512 rows and 512 columns of pixels. If the image reconstruction algorithm were applied to the acquired images in their entirety, it would result in the processing of about 128 million voxels, which is too high a number and in any case would not be very useful, since the vascular structures that generally need to be displayed typically occupy about 2% of the virtual volume.
Also, it has been proposed to reduce the resolution value of the acquired images, by calculating averages of four pixels, in order to arrive at a resolution value of 256, which results in a reduction of the virtual volume. After a first iteration of the algorithm performed on each image, a first rough representation of the location of the objects of interest is already obtained, making it possible to select, for the subsequent iterations, a subset of p voxels and to eliminate the others. Each of these remaining p voxels is then subdivided into eight, so that the projection of such a subdivided voxel corresponds to xc2xd a pixel of resolution 256, i.e., a pixel of resolution 512. The sub-sequent iterations of the algorithm, in practice two iterations, are then performed on all of these subdivided voxels.
Even after the elimination of a certain number of voxels, the set of subdivided voxels amounts to about 32 million, which is still a very high number, and which translates into a non-negligible cost in terms of calculation time. One solution could consist of eliminating more voxels in order to further reduce the number of subdivided voxels remaining. But if this route is taken, artifacts are produced in the images displayed, due to the underrepresentation of the volume of the data handled by the image reconstruction algorithm.
An embodiment of the invention reduces the calculation time of the processor implementing the image reconstruction algorithm while not modifying the quality of the images obtained, i.e., by specifically not introducing artifacts into the images.
An embodiment of the invention is a process for reconstructing a three-dimensional image of an object from a set of numbered projected two-dimensional images of the object obtained from various positions of an imaging apparatus around the object. This process comprises a calibration of the apparatus in which a virtual volume surrounding the object is generated and broken down into voxels, an acquisition of the set of numbered projected two-dimensional images, and a reconstruction of the three-dimensional image from the projected acquired two-dimensional images, and from an iterative algebraic image reconstruction algorithm.
According to an embodiment of the invention, a first iteration of the algorithm is performed with a predetermined initial image resolution so as to obtain, at the end of this first iteration, first density values for the voxels of said volume. At least one part of the voxels of the virtual volume are subdivided into several sets, respectively corresponding to different image resolutions that are multiples or sub-multiples of the initial resolution. And during each subsequent iteration of the algorithm, the algorithm is successively applied to each of the sets of voxels.
In other words, an embodiment of the invention makes it possible to apply the iterative algebraic image reconstruction algorithm to a multi-resolution volume. In this volume, voxels which a priori represent the objects of interest to be displayed are selected, and they are divided in order to increase the resolution. The other voxels, which are of less interest since they do not directly relate to the objects to be displayed, are either left as is, or regrouped at least once in order to reduce the value of the resolution, but they are still used for the image reconstitution calculations, making it possible to ultimately obtain images of very good quality with a reduced calculation time.
According to one mode of implementation of the invention, during each subsequent iteration of the algorithm, i.e., during each iteration beginning with the second one, a virtual image is determined for each projected acquired image by successively combining the elementary virtual images respectively obtained from the projections of the corresponding sets of voxels into the acquisition plane of the projected acquired image.
More precisely, in an embodiment of the invention and particularly in order to further reduce the calculation time, the elementary virtual images are preferably generated in the increasing order of the resolution values, beginning with the elementary virtual image corresponding to the lowest resolution value (for example 64), and after an elementary virtual image is determined, a scaling is performed in order to obtain a so-called xe2x80x9cenlargedxe2x80x9d virtual image whose resolution corresponds to that of the next elementary virtual image to be determined, and said enlarged virtual image is combined with the next elementary virtual image.
Generally, according to one mode of implementation of the invention, projected two-dimensional having a predetermined base resolution (for example r=512) are acquired. An initial resolution is chosen which is equal to a sub-multiple of the base resolution (for example r/2=256), and chosen from among said different image resolutions are said base resolution (r), the initial resolution (r/2) and at least one first additional resolution (for example (r/4=128), which is a sub-multiple of the initial resolution (r/2).
According to one mode of implementation of the invention, a first density threshold is generated as a function of a predetermined selection criterion. Each voxel having a density higher than or equal to the first threshold is subdivided into a first number of subdivided voxels, the first number (typically 8) being defined based on the relationship between the base resolution and the initial resolution, all of which sub-divided voxels form a first set of voxels corresponding to said base resolution (r=512). At least some of the voxels whose density is lower than the first threshold, and which meet a predetermined regrouping criterion, are regrouped so as to form regrouped voxels which form a second set of voxels corresponding to the first additional resolution (r/4=128), the number (typically 8) of regrouped voxels in each group being based on the relationship between the initial resolution (r=256) and the first addition-al resolution (128). And, the voxels whose density is lower than the first threshold, and which do not meet the predetermined regrouping criterion, form a third set of voxels corresponding to the initial resolution (256).
By way of example, a voxel meets the regrouping criterion if each of the coordinates of the center of the voxel is a multiple of 2 and if the density of each voxel adjacent to said voxel is lower than the first threshold.
It is also possible, and preferable, to once again regroup the voxels which have already been regrouped and which meet the regrouping criterion, in order to form a fourth set of voxels corresponding to a second additional resolution (for example 64), which is a sub-multiple of the first additional resolution (for example 128).
Generally, the part of the voxels of the virtual volume that is subdivided can be obtained by eliminating the voxels located in a layer of predetermined thickness of the surface of the volume. It has actually been observed that the image reconstruction algorithm tends to create high densities on the periphery of the volume, which do not in fact correspond to objects of interest to be displayed.
It is also possible to eliminate from the virtual volume the isolated voxels whose density is higher than a second predetermined threshold. In fact, it has been observed that an isolated voxel of high density does not correspond to an object of interest.
Furthermore, after the first iteration of the algorithm, each voxel whose density value is higher than or equal to a third predetermined threshold is preferably assigned a density value equal to the maximum density value obtained among the density values of said voxel and the adjacent voxels. In other words, at this point an expansion of the high-density voxels is preferably performed, in order to further improve the quality of the display of the objects of interest.